Density-matrix renormalization-group study of the polaron problem in the Holstein model

We propose a density-matrix renormalization-group (DMRG) approach to study lattices including bosons. The key to the approach is an exact mapping of a boson site containing $2^N$ states to $N$ pseudosites, each with 2 states. The pseudosites can be viewed as the binary digits of a boson level. We apply the pseudosite DMRG method to the polaron problem in the one- and two-dimensional Holstein models. Ground-state results are presented for a wide range of electron-phonon coupling strengths and phonon frequencies on lattices large enough (up to 80 sites in one dimension and up to $20\times 20$ sites in two dimensions) to eliminate finite-size effects, with up to 128 phonon states per phonon mode. We find a smooth but quite abrupt crossover from a quasi-free-electron ground state with a slightly renormalized mass at weak electron-phonon coupling to a polaronic ground state with a large effective mass at strong coupling, in agreement with previous studies.